相关论文: A novel second-order nonstandard finite difference…
This paper introduces a novel approach to evaluating the asymptotic stability of equilibrium points in both continuous-time (CT) and discrete-time (DT) nonlinear autonomous systems. By utilizing indirect Lyapunov methods and linearizing…
This study debuts a new spline dimensional decomposition (SDD) for uncertainty quantification analysis of high-dimensional functions, including those endowed with high nonlinearity and nonsmoothness, if they exist, in a proficient manner.…
\noindent Using the techniques connected with the measure of noncompactness we investigate the neutral difference equation of the following form \begin{equation*} \Delta \left(r_{n}\left(\Delta \left(x_{n}+p_{n}x_{n-k}\right) \right)…
We present a sharp collocated projection method for solving the immiscible, two-phase Navier-Stokes equations in two- and three-dimensions. Our method is built using non-graded adaptive quadtree and octree grids, where all of the fluid…
In this paper, high order well-balanced finite difference weighted essentially non-oscillatory methods to solve general systems of balance laws are presented. Two different families are introduced: while the methods in the first one…
We establish the existence of non-stationary solutions to a symmetric system of second-order autonomous differential equations. Our technique is based on the equivariant degree theory and involves a novel characterization of orbit types of…
We propose a novel direct transcription and solution method for solving nonlinear, continuous-time dynamic optimization problems. Instead of forcing the dynamic constraints to be satisfied only at a selected number of points as in direct…
It is often unnoticed that the predominant way to use collocation methods is fundamentally flawed when applied to optimal control in robotics. Such methods assume that the system dynamics is given by a first order ODE, whereas robots are…
Using the method of equivariant moving frames, we present a procedure for constructing symmetry-preserving finite element methods for second-order ordinary differential equations. Using the method of lines, we then indicate how our…
This paper presents a novel numerical optimisation method for infinite dimensional optimisation. The functional optimisation makes minimal assumptions about the functional and without any specific knowledge on the derivative of the…
This article addresses a new class of fractional nonlocal neutral stochastic differential system of order 1<q<2 including non-instantaneous impulses(NIIs) and state-dependent delay(SDD) with the Poisson jumps and the Wiener process in…
In this paper, we propose and analyze a second order accurate (in both time and space) numerical scheme for the Poisson-Nernst-Planck-Navier-Stokes system, which describes the ion electro-diffusion in fluids. In particular, the…
This paper studies adaptive first-order least-squares finite element methods for second-order elliptic partial differential equations in non-divergence form. Unlike the classical finite element method which uses weak formulations of PDEs…
The problem of increasing the accuracy of an approximate solution is considered for boundary value problems for parabolic equations. For ordinary differential equations (ODEs), nonstandard finite difference schemes are in common use for…
The paper explores the differential inclusion of a special form. It is supposed that the support function of the set in the right-hand side of an inclusion may contain the maximum of the finite number of continuously differentiable (in…
This paper introduces alternating-direction implicit (ADI) solvers of higher order of time-accuracy (orders two to six) for the compressible Navier-Stokes equations in two- and three-dimensional curvilinear domains. The higher-order…
Many successful methods to learn dynamical systems from data have recently been introduced. However, ensuring that the inferred dynamics preserve known constraints, such as conservation laws or restrictions on the allowed system states,…
This work investigates a dynamical system functioning as a nonsmooth adaptation of the continuous Newton method, aimed at minimizing the sum of a primal lower-regular and a locally Lipschitz function, both potentially nonsmooth. The…
In this paper, we develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations (PDEs) with uncertainties. The new approach is realized in the semi-discrete finite-volume framework and is based…
In this paper, we propose some algorithms for analytical solution construction to nonlinear polynomial partial differential equations with constant function coefficients. These schemes are based on one-(single), two- (double) or three-…